American Mathematical Society TranslationsSeries 2 Advances in the Mathematical Sciences 1998; 197 pp; hardcover Volume: 182 ISBN10: 0821841130 ISBN13: 9780821841136 List Price: US$108 Member Price: US$86.40 Order Code: TRANS2/182
 This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method. Readership Graduate students and research mathematicians interested in the theory of nonlinear waves and its applications. Table of Contents  A. M. Balk and E. V. Ferapontov  Invariants of wave systems and web geometry
 A. M. Balk and V. E. Zakharov  Stability of weakturbulence Kolmogorov spectra
 V. A. Kalmykov  Energy transfer in the spectrum of surface gravity waves by resonance five wavewave interactions
 E. Kartashova  Wave resonances in systems with discrete spectra
 L. I. Piterbarg  Hamiltonian formalism for Rossby waves
 V. E. Zakharov  Weakly nonlinear waves on the surface of an ideal finite depth fluid
